Infinite-Dimensional Dynamical Systems

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April 2001



This book treats the theory of global attractors, a recent development in the theory of partial differential equations.


Part I. Functional Analysis: 1. Banach and Hilbert spaces; 2. Ordinary differential equations; 3. Linear operators; 4. Dual spaces; 5. Sobolev spaces; Part II. Existence and Uniqueness Theory: 6. The Laplacian; 7. Weak solutions of linear parabolic equations; 8. Nonlinear reaction-diffusion equations; 9. The Navier-Stokes equations existence and uniqueness; Part II. Finite-Dimensional Global Attractors: 10. The global attractor existence and general properties; 11. The global attractor for reaction-diffusion equations; 12. The global attractor for the Navier-Stokes equations; 13. Finite-dimensional attractors: theory and examples; Part III. Finite-Dimensional Dynamics: 14. Finite-dimensional dynamics I, the squeezing property: determining modes; 15. Finite-dimensional dynamics II, The stong squeezing property: inertial manifolds; 16. Finite-dimensional dynamics III, a direct approach; 17. The Kuramoto-Sivashinsky equation; Appendix A. Sobolev spaces of periodic functions; Appendix B. Bounding the fractal dimension using the decay of volume elements.
EAN: 9780521635646
ISBN: 0521635640
Untertitel: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors. 'Cambridge Texts in Applied Mathematics'. 14 b/w illus. Sprache: Englisch.
Verlag: Cambridge University Press
Erscheinungsdatum: April 2001
Seitenanzahl: 480 Seiten
Format: kartoniert
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